# Half Life help

1. Feb 27, 2005

### parwana

At a certain temperature the reaction

2N2O5 --> 4NO2 + O2

is a first order reaction with t1/2 = 153.0 sec

What is the rate constant for this reaction (1/sec) ?

Ok I know the equation is t1/2= ln2/k

so isnt k the rate constant, and wouldnt the answer be ln2/153 sec= .0045??

2. Feb 27, 2005

### Staff: Mentor

The first order equation is -

$\frac{d [A]}{dt} = - k [A]$

where k is the rate constant.

The solution, as you correctly mentioned, is -

$ln \frac{[A]}{[A_o]} = - k t$, where [A] is the concentration at time t, and Ao is the initial concentration, at t=0.

The definition of half-life is-

$ln \frac{[A_o]/2}{[A_o]} = - k t_{1/2}$, or

ln 2 = k t1/2